An introduction to $C^*$-algebras and $K$-theory II
This course extends the introductory study of $C^*$-algebras and $K$-theory introduced last semester, with a focused emphasis on classification of $C^*$-algebras using K-theoretic data. The interplay between functors $K_0$ and $K_1$ will be explored. Computational examples will be provided throughout the course, together with applications relevant to the classification of $C^*$-algebras.
讲师
日期
2025年02月17日 至 05月18日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周四 | 14:20 - 16:05 | A3-1-301 | ZOOM 06 | 537 192 5549 | BIMSA |
修课要求
Undergraduate Functional Analysis, General Topology, Algebra, An introduction to $C^*$-algebras and $K$-theory
课程大纲
1. Review of fundamental concepts of $C^*$-algebras and $K$-groups
2. The index map
3. The higher $K$-functors
4. Bott periodicity
5. The six-term exact sequence
6. Related topics (tensor product, etc.) in theory of $C^*$-algebras
7. Other topics in $K$-theory and classification
2. The index map
3. The higher $K$-functors
4. Bott periodicity
5. The six-term exact sequence
6. Related topics (tensor product, etc.) in theory of $C^*$-algebras
7. Other topics in $K$-theory and classification
参考资料
1. Gerard Murphy, $C^*$-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990. MR1074574 (91m:46084)
2. Mikael Rørdam, Flemming Larsen, and Niels Laustsen, An introduction to K-theory for $C^*$-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000. MR1783408 (2001g:46001)
3. Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
4. Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
5. John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
6. Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
2. Mikael Rørdam, Flemming Larsen, and Niels Laustsen, An introduction to K-theory for $C^*$-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000. MR1783408 (2001g:46001)
3. Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
4. Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
5. John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
6. Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
听众
Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
不公开
笔记公开
不公开
语言
英文
讲师介绍
贺卓丰2018年毕业于东京大学，后成为该校副研究员。2022年华东师范大学博士后出站，2023年加入北京雁栖湖应用数学研究院任助理研究员。现在的研究兴趣包括C*代数的分类理论、C*动力系统和拓扑动力系统。